Intro to Differential Equations Problem #1

[JosephK]

Homework Statement

1. Find the general solution to the differential equation:
y''-5y'+6y = 0

Homework Equations

The Attempt at a Solution

m^2 - 5m + 6 = 0
(m-1)(m-5) = 0
y' = Ae^x+Be^5x

 

[Mark44]

Homework Statement

1. Find the general solution to the differential equation:
y''-5y'+6y = 0

Homework Equations

The Attempt at a Solution

m^2 - 5m + 6 = 0
(m-1)(m-5) = 0

Your factorization is incorrect. (m - 1)(m - 5) = m² - 6m + 5, not m² - 5m + 6.

y' = Ae^x+Be^5x

 

[JosephK]

This cannot be factored.

 

[Mark44]

This cannot be factored.

(m - 3)(m - 2) ?

 

[JosephK]

So the answer to this differential equation is

y = c1e^3x+c2e^2x?

 

[Mark44]

Yes, and you can check for yourself that your solution satisfies the differential equation. It's always a good idea to check.